Apparatus for determining properties of an electrically conductive object

ABSTRACT

Eddy currents are generated in an object constructed of a conductive material by transmitting an electromagnetic signal to the object and detecting electromagnetic signals generated by eddy currents induced in the object, and an electromagnetic signal V(t) is described by a product of two factors F and G(t), wherein F is a function of the geometry and electrical and magnetic properties of the material and G(t) is a function of geometry of the material, the electrical and magnetic properties of the material, the thickness perpendicular to the surface of the material, and time.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to a method for describing an electromagneticsignal generated by eddy currents in a conductive material.

Such a method can be used inter alia in determining properties of anelectrically conductive measuring object composed of that material. Thisinvention relates in particular to a method for determining propertiesof an electrically conductive measuring object, wherein:

a. utilizing at least one transmitting antenna, an electromagnetic fieldchanging over time is emitted to the measuring object for generatingeddy currents in the object;

b. utilizing at least one receiving antenna, the electromagnetic signalgenerated by the eddy currents is detected; and

c. on the basis of the detected electromagnetic signal, the propertiesof the measuring object are determined.

This invention further relates to an apparatus for practising such amethod.

2. Description of Related Art

Such a method and apparatus are known from, for instance, U.S. Pat. No.4,843,319. In this known method and apparatus, by means of atransmitting coil, a pulsated electromagnetic field is generated in thematerial of the measuring object. This gives rise to time-dependent eddycurrents in the material. These eddy currents are detected by means of areceiving coil. The eddy currents, which change with time, cause achanging magnetic flux through the receiving coil, so that an inductionvoltage prevails across the receiving coil. Utilizing an amplifier, thischanging induction voltage can be registered as a function of time.Thus, the electromagnetic signal generated by the eddy currents isdetected as a function of the time t.

With the known apparatus, it is stated that the time-dependent behaviorof the signal for small times t is determined by a constant logarithmicrate of decay of about 1.5. In other words, the received signal can bedescribed with a signal V(t), to which the following relation applies:d(1n V)/d(1n t)=−1.5.

Beyond a certain critical time, designated τ and which is directlyproportional to the square of the thickness of the surface of thematerial of the object under examination, so that τ=cd², the logarithmicrate of decay falls to a lower value which equals A−2.171n(t). In otherwords, the following applies where t is greater than τ: d(1n V)/d(1nt)=A−2.171n(t). Here A is determined by the material properties and thegeometry of the measuring object. Accordingly, before the thickness ofthe measuring object can be determined, first the constants c and A areto be determined. Determining the constants c and A is carried outthrough two measurements on two different test objects of the samematerial but having different, homogeneous wall thicknesses. This meansthat for carrying out the method, at all times two mutually differenttest specimens are to be at hand. Further, in this known method andapparatus, from a single measurement, only the homogeneous wallthickness of the material can be computed. Furthermore, the apparatus islimited to the use of a receiving coil for measuring the signal.

SUMMARY OF THE INVENTION

The invention contemplates a solution to the disadvantages outlinedabove. Accordingly, an object of the invention is to provide a methodand apparatus wherein for detecting the wall thickness of a measuringobject, only a single measurement on a test object is to be performedbeforehand. Another object of the invention is to make it possible todetermine the distribution of wall thicknesses of the material of themeasuring object. A further object of the invention is to determine,instead of the wall thicknesses, the permeability and the conductivityof the material of the measuring object. It is even possible todetermine the spread in the conductivity or the spread in the relativepermeability of the material. In order to provide a basis for carryingout such methods, the method for describing an electromagnetic signalgenerated by eddy currents in an electrically conductive material ischaracterized, according to the invention, in that the signal V(t) isdescribed by at least one product of two factors F and G(t), where F isa function of the geometry of the material and the electrical andmagnetic properties of the material, and where G(t) is a function of thegeometry of the material, the electrical and magnetic properties of thematerial, the thickness perpendicular to the surface of the material andtime.

The method according to the invention, in which said description of thesignal is utilized for determining properties of an electricallyconductive measuring object, is characterized in that utilizing apredetermined algorithm, parameters $\frac{\sigma_{i}}{\mu_{i}}$

or parameters to be derived from these parameters of the equation$\begin{matrix}{{V(t)} = {\sum\limits_{i = 1}^{n}{\theta_{i}F_{i}{G_{i}(t)}}}} & (1)\end{matrix}$

or equation to be derived therefrom, with $\begin{matrix}{F_{i} = {\delta \sqrt{\frac{\sigma_{i}}{\mu_{i}}}}} & (2) \\{{G_{i}(t)} = \frac{t^{\gamma}}{1 + {{\alpha \left( {\beta \frac{t}{\tau_{i}}} \right)}^{m}^{\beta \frac{t}{\tau_{i}}}}}} & (3)\end{matrix}$

i=1, 2, . . . n   (4)

and

$\begin{matrix}{{\sum\limits_{i = 1}^{n}\theta_{i}} = 1} & (5)\end{matrix}$

are selected such that V(t) according to a predetermined criterion ofthe algorithm corresponds to the course over time of the detectedelectromagnetic signal, where α, β, γ, δ and m are real numbers whichare dependent on the geometry of the measuring object, the transmittingantenna and the receiving antenna, as well as on the relative positionsof the object, the transmitting antenna and the receiving antenna, μ_(i)represents the magnetic permeability of an area i of the measuringobject and σ_(i) represents the electrical conductivity of the area i ofthe measuring object, and the areas i (i=1, 2, . . . , n) togethergenerate the detected electromagnetic signal.

When with this method the thickness d_(i) of the material is to bedetermined, it is necessary only once, using a test object, to determinethe magnetic permeability and the electrical conductivity of thematerial. The values of α, β, γ, δ and m can, in principle, given aknown geometry of the transmitting antenna, receiving antenna and theobject, be priorly calculated on the basis of a simulation model. Whenthe conductivity or relative permeability is known, it is possible,using the method outlined above, to determine the wall thickness of thematerial on the basis of the formula τ_(i)=μ_(i)σ_(i)d_(i) ² with i=n=1.It is also possible to determine the distribution of wall thicknesses ofthe material, given a known conductivity and a known relativepermeability of the material, with n≧2.

The invention further makes it possible to determine the conductivityand the relative permeability of the material, given a known wallthickness. It is even possible to determine the spread in theconductivity or the spread in the relative permeability of the material,given a known wall thickness.

BRIEF DESCRIPTION OF THE DRAWINGS

The above will be further explained with reference to the drawing, inwhich:

FIG. 1 shows a possible embodiment of an apparatus according to theinvention for practising a method according to the invention on ameasuring object; and

FIG. 2 shows a possible embodiment of a test object.

DETAILED DESCRIPTION

The apparatus 1 according to FIG. 1 comprises a transmitting antenna 2in the form of a coil which is coupled to a transmitter unit 4. Further,the apparatus comprises a receiving antenna 6, similarly in the form ofa receiving coil, which is coupled to a receiver unit 8. The transmitterunit 4 and the receiver unit 8 are coupled to a computer 10.

The apparatus further comprises an input unit 12, in this example akeyboard, and a display 14, each connected to the computer 10.

FIG. 1 further shows a measuring object 16. Properties of the measuringobject, such as its thickness, magnetic permeability and electricalconductivity, can be measured by means of the apparatus 1. If thethickness, the magnetic permeability and the electrical conductivity arethe same throughout, the entire measuring area, which is designated inFIG. 1 by the arrow 22, can be considered homogeneous. It is alsopossible, however, that within the measuring area 22 differentthicknesses occur, for instance a thickness d_(i=1) in the area i=1,which is indicated in FIG. 1 by the arrows 18, and a thickness d_(i=2)in the area i=2, which is indicated in FIG. 1 by the arrow 20. Also,,the thickness may be the same throughout, while in the area i=1 themagnetic permeability μ_(i=1) and/or the electrical conductivity σ_(i=1)differs from the magnetic permeability μ_(i=2) and/or the electricalconductivity σ₁₌₂ in the area i=2.

The operation of the apparatus is as follows. Using the transmitter unit4 and the transmitting coil 2, a pulsating electromagnetic field isgenerated in the measuring area 22 of the object 16. In this example,the assumption is that a pulse to the generated electromagnetic fieldcan be described with the ideal dirac pulse. However, this is notnecessary to the invention.

The electromagnetic field thus generated in the measuring area 22 andvarying, will have as a result that eddy currents are generated.According to Lenz's law, the flow of those eddy currents is such thatthe change of the electromagnetic field is counteracted. These eddycurrents, in turn, generate a changing electromagnetic field, so thataccording to Faraday's law an induction voltage arises on the receivingcoil 6. In other words, the receiving coil 6 detects an electromagneticsignal that is generated by the eddy currents. This electromagneticsignal is measured by means of the receiver unit 8 and applied to thecomputer 10. The measured electromagnetic signal is here described withS(t). In all particular embodiments of the method according to theinvention to be described in more detail hereinafter, the assumption isthat the measured signal S(t) can be described by a signal V(t) whichcomprises at least one product of two factors F and G(t), where F is afunction of the geometry of the measuring object 16 and the electricaland magnetic properties of the material of the measuring object 16. G(t)is also a function of the geometry of the measuring object 16, theelectrical and magnetic properties of the material of the measuringobject 16, the thickness perpendicular to the surface 24 of themeasuring object 16 and time.

Because the changing electromagnetic field is emitted using thetransmitting antenna 2 and because the electromagnetic signal isdetected using the receiving antenna 6, factors F and G are each also afunction of the geometry of the transmitting and receiving antennas, aswell as of the relative positions of the transmitting antenna, thereceiving antenna and the measuring object.

More particularly, according to the invention, the followingapproximation for the signal V(t) has been found: $\begin{matrix}{{{V(t)} = {\sum\limits_{i = 1}^{n}{\theta_{i}F_{i}{G_{i}(t)}}}}{with}} & (1) \\{{F_{i} = {\delta \sqrt{\frac{\sigma_{i}}{\mu_{i}}}}}{and}} & (2) \\{{G_{i}(t)} = \frac{t^{\gamma}}{1 + {{\alpha \left( {\beta \frac{t}{\tau_{i}}} \right)}^{m}^{\beta \frac{t}{\tau_{i}}}}}} & (3)\end{matrix}$

where α, β, γ, δ and m are dependent on the geometry of the material,σ_(i) represents the conductivity of an area i of the material and μ_(i)represents the magnetic permeability of the area i of the material, andthe areas i (i=1, 2, . . . , n) together generate the signal V(t). Hereα, β, γ, δ and m are also dependent on the geometry of the transmittingantenna and receiving antenna, as well as on the relative positions ofthe material, the transmitting and the receiving antenna.

If the above-mentioned method for describing the electromagnetic signalgenerated by the eddy currents is used, the following method fordetermining properties of the object can be carried out.

Using a predetermined algorithm, parameters τ_(i) and/or$\frac{\sigma_{i}}{\mu_{i}}$

or parameters to be derived from these parameters of the equation$\begin{matrix}{{V(t)} = {\sum\limits_{i = 1}^{n}{\theta_{i}F_{i}{G_{i}(t)}}}} & (1)\end{matrix}$

or an equation to be derived therefrom, with $\begin{matrix}{F_{i} = {\delta \sqrt{\frac{\sigma_{i}}{\mu_{i}}}}} & (2) \\{{G_{i}(t)} = \frac{t^{\gamma}}{1 + {{\alpha \left( {\beta \frac{t}{\tau_{i}}} \right)}^{m}^{\beta \frac{t}{\tau_{i}}}}}} & (3)\end{matrix}$

i=1, 2, . . . n   (4)

and $\begin{matrix}{{\sum\limits_{i = 1}^{n}\theta_{i}} = 1} & (5)\end{matrix}$

are selected such that V(t), according to a predetermined criterion ofthe algorithm, corresponds to the course over time of the detectedelectromagnetic signal.

Suppose, for instance, that the thickness d of the measuring area 22 ofthe measuring object 16 is to be determined. The assumption is that thethickness d is uniform, that is, d₁=d₂=d. Because the geometry of themeasuring object 16, the transmitting antenna 2, the receiving antenna 6and their relative positions in this example are known, α, β, γ, δ and mcan be calculated in a manner known per se, using a simulation model.These parameters can therefore be assumed to be known. It is alsoassumed that the material of the measuring object is homogeneous. Inother words, the magnetic permeability and the electrical conductivityare the same in the entire measuring area 22. This means that in itselfno distinction needs to be made between signals coming from the area i=1on the one hand and the area i=2 on the other. In the above-mentionedformula 1, therefore, i=n=1 can be selected. The magnetic permeabilityμ₁ of the material will hereinafter be designated μ₀, while theconductivity σ₁ of the material will hereinafter be designated σ₀.

First of all, μ₀ or σ₀ is to be determined on the basis of a calibrationmeasurement. This calibration measurement is carried out as follows.

The measuring object 16 is replaced by a test object 26 (see FIG. 2)whose thickness do is known. Then the apparatus 1 is activated. Itmeasures the signal G(t) coming from the test object 26. The computer 10then selects, according to a predetermined algorithm, the parameters μ₀and σ₀ such that according to a predetermined criterion of thealgorithm, V(t) corresponds to the course over time of theelectromagnetic signal S(t) generated by the eddy currents in the testobject and detected by the receiving antenna 4. Further, according tothe invention, τ_(i)=μ_(i)σ_(i)d_(i) ² (6). Because i=n=1, it followsfrom formula 6 that τ₁=μ₀σ₀d₀ ². By substituting τ₁ in formula 1 byμ₀σ₀d₀ ², it is possible, for instance according to theLevenberg-Marquardt algorithm, to determine μ₀ and σ₀ such that V(t)corresponds accurately to S(t). Thus, μ₀ and σ₀ have been determined.

The test object 26 is then replaced by the measuring object 16. Again,using the transmitting antenna 2, a changing electromagnetic field isgenerated. Again, the electromagnetic signal S(t) subsequently detectedby the receiver unit 8 is applied to the computer 10. Then theparameters τ₁ and $\frac{\sigma_{1}}{\mu_{1}}$

(or parameters which can be derived therefrom) of the equation$\begin{matrix}{{V(t)} = {\sum\limits_{i = 1}^{n}{\theta_{i}F_{i}{G_{i}(t)}}}} & (1)\end{matrix}$

or an equation derivable therefrom, with $\begin{matrix}{F_{i} = {\delta \sqrt{\frac{\sigma_{i}}{\mu_{i}}}}} & (2) \\{{G_{i}(t)} = \frac{t^{\gamma}}{1 + {{\alpha \left( {\beta \frac{t}{\tau_{i}}} \right)}^{m}^{\beta \frac{t}{\tau_{i}}}}}} & (3)\end{matrix}$

i=n=1   (4)

and

θ₁=1   (5)

are selected such that V(t), according to a predetermined criterion ofthe algorithm, corresponds to the course over time of the detectedelectromagnetic signal S(t).

Thus, τ₁ and $\frac{\sigma_{1}}{\mu_{1}}$

of the measuring object have been determined. Further, according toformula 6, τ₁σ₁d₁ ². This means that d₁ can be determined on the basisof the τ₁ and $\frac{\sigma_{1}}{\mu_{1}}$

found, and on the basis of the known value μ₁=μ₀ or σ₁=σ₀. The thusobtained value of d₁ corresponds to the homogeneous thickness d₀ of thematerial.

It may also happen, however, that the material of the measuring object16 includes a defect or flaw. In that case, the thickness of themeasuring object is not the same throughout. In the example of FIG. 1,the assumption was that the thickness in the areas i=1 equals d₁, whilethe thickness in the area i=2 equals d₂. The values for d₁ and d₂ canpresently be determined as follows.

In formula 1, n is selected to be greater than or equal to 2. In thisexample, n is selected to be, for instance, 4. Again, the assumption isthat the magnetic and electrical properties of the material arehomogeneous. In other words, μ₁=μ₂=μ₃=μ₄=μ₀ and σ₁σ₂=σ₃=σ₄=σ₀. μ₀ andσ₀, as has been discussed above, can again be determined using a testobject. Then, using the predetermined algorithm, the parameters τ_(i)and $\frac{\sigma_{i}}{\mu_{i}}$

(or parameters that can be derived therefrom) of the equation$\begin{matrix}{{V(t)} = {\sum\limits_{i = 1}^{n = 4}{\theta_{i}F_{i}{G_{i}(t)}}}} & (1)\end{matrix}$

or an equation to be derived therefrom, with $\begin{matrix}{F_{i} = {\delta \sqrt{\frac{\sigma_{i}}{\mu_{i}}}}} & (2) \\{{G_{i}(t)} = \frac{t^{\gamma}}{1 + {{\alpha \left( {\beta \frac{t}{\tau_{i}}} \right)}^{m}^{\beta \frac{t}{\tau_{i}}}}}} & (3)\end{matrix}$

i=1, 2, . . . n=4   (4)

and

$\begin{matrix}{{\sum\limits_{i = 1}^{n = 4}\theta_{i}} = 1} & (5)\end{matrix}$

are selected such that V(t), according to a predetermined criterion ofthe algorithm, corresponds to the course over time of the detectedelectromagnetic signal S(t).

Again, for fitting the parameters of the model, use is made of theLevenberg-Marquardt algorithm. If the material is indeed homogeneous, itwill appear that the determined ratio of μ_(i) and σ_(i) corresponds foreach i to the ratio of μ₀ and σ₀. Obviously, it is also possible informula 1 for each i to directly replace the ratio of μ_(i) and σ_(i) bythe known ratio of μ₀ and μ₀. In that case, using the algorithm, onlythe parameter τ_(i) for i=1-4 and θ_(i) for i=1-4 is determined.Physically, of the measuring area 22, the fraction θ₁F₁G₁(t) can beregarded as the signal generated by the area i=1, while the signalθ₂F₂G₂(t) comes from the area i=2. Further, in this example, thealgorithm will yield that the parameters θ₃ and θ₄ are substantiallyequal to 0, because only two different thicknesses occur in themeasuring area 22. The signal θ₁F₁G₁(t) can then be taken as the signalcoming from the relatively large area i=1 of the thickness d₁, while thesignal θ₂F₂G₂(t) comes from the relatively small area i=2 of a lesserthickness d₂. The area i=2 of the lesser thickness then includes aso-called defect.

Then, on the basis of the values of τ₁ and τ₂, the thickness d₁ and thethickness d₂ are determined, using the formula τ_(i)=μ_(i)σ_(i)d_(i) ².Here, it can again be stated that μ_(i)=μ₀ and σ_(i)=σ₀.

Using the apparatus according to FIG. 1, it is also possible todetermine the permeability μ₀ and the conductivity σ₀ of a homogeneousmaterial. Such a determination corresponds to the above-discussedcalibration.

When the material is inhomogeneous, either spread in the conductivity orspread in the relative permeability of the material, given a known wallthickness, can be determined. This can be done as follows.

Suppose that the material of FIG. 1 satisfies d₁=d₂=d₀. Further, thepermeability μ₁ of the area i=1 is equal to the permeability μ₂ of thearea i=2. In other words, the permeability equals μ₀. On the basis ofthe formula τ_(i)=μ_(i)σ_(i)d_(i) ², τ_(i) can be expressed in σ_(i).Thus, τ_(i)=μ₀σ_(i)d₀ ². This value of τ_(i) can presently besubstituted in formula 1. Formula 1 presently contains the variablesθ_(i) and σ_(i). In accordance with the invention, these variables canbe fitted to the measured signal S(t).

Fitting is carried out, for instance, for n=3. Thus, values are foundfor θ₁, θ₂ and θ₃, and for σ₁, σ₂ and σ₃. Here, θ₃ will be substantiallyequal to 0, since in the measuring object in this example, in goodapproximation, two different conductivities occur, viz. σ₁ for the areai=1 and σ₂ for the area i=2. The values found for σ₁ and σ₂ represent aspread in the conductivity in the material. Entirely analogously, aspread in the permeability can be calculated if the wall thickness isequal to d₀ throughout, and the conductivity is equal to σ₀ throughout.Such variants are all understood to fall within the scope of theinvention.

In carrying out the above-mentioned measurements, the assumption is thatthe parameters depending on the geometry do not change. It is alsopossible, however, to assume that the parameters change in a knownmanner. In that case, in the measurement, the signal strength isdetermined. On the basis thereof, the lift-off can be calculated. Thelift-off is the distance between, on the one hand, the receiving andtransmitting antennas arranged in mutual proximity and, on the other,the surface of the measuring object. Then, on the basis of the lift-off,the correct model parameters (α, β, γ, δ and m) can be calculated, givena known geometry. This calculation can then be a function of thedistance mentioned. If the geometry of the object and/or thetransmitting and receiving antennas is not known, the model parametersα, β, γ, δ and m cannot be calculated. It is possible, however, asdiscussed above, using a test object, to determine the model parametersα, β, γ, δ and m for a number of mutually different distances. On thebasis of the different values that are found for the model parametersfor different distances, it is possible to determine in a manner knownper se a model in which the model parameters are a linear function ofthe distance mentioned.

Such variants are all understood to fall within the scope of theinvention.

What is claimed is:
 1. A method for determining properties of anelectrically conductive object to be measured, comprising the steps of:transmitting a time varying electromagnetic field from a transmitantenna to said object for generating eddy currents in said object;detecting an electromagnetic signal S(t) generated by said eddy currentsusing a receiving antenna; and determining properties of said objectfrom said signal S(t) by selecting certain τ_(i) and$\frac{\sigma_{i}}{\mu_{i}}$

 such that $\begin{matrix}{{{S(t)} = {\sum\limits_{i = 1}^{n}{\theta_{i}F_{i}{G_{i}(t)}}}}{with}} & (1) \\{F_{i} = {\delta \sqrt{\frac{\sigma_{i}}{\mu_{i}}}}} & (2) \\{{G_{i}(t)} = \frac{t^{\gamma}}{1 + {{\alpha \left( {\beta \frac{t}{\tau_{i}}} \right)}^{m}^{\beta \frac{t}{\tau_{i}}}}}} & (3)\end{matrix}$

i=1, 2, . . . n   (4)  and $\begin{matrix}{{\sum\limits_{i = 1}^{n}\theta_{i}} = 1} & (5)\end{matrix}$

wherein α, β, γ, δ, and m are real numbers dependent on geometry of saidobject, of said transmitting antenna and of said receiving antenna;wherein said real numbers are further dependent on relative positions ofsaid object, said transmitting antenna and said receiving antenna;wherein μ_(i) represents magnetic permeability of an area i of saidobject and σ_(i) represents electrical conductivity of an area i of saidobject; and wherein said areas i (i=1, 2, . . . n) together generatesaid electromagnetic S(t).
 2. The method in accordance with claim 1 andfurther comprising the step of selecting i=n=1 and wherein μ_(i)=μ₀ andis a known value, and wherein said thickness d_(i) of an area i of saidobject is determined from equation τ_(i)=μ_(i)σ_(i)d_(i) ².
 3. Themethod in accordance with claim 1 and further comprising the steps ofselecting i=n=1 and wherein σ₁=σ₀ is a known value and wherein saidthickness d_(i) of an area i of said object is determined from equationτ_(i)=μ_(i)σ_(i)d_(i) ².
 4. The method in accordance with claim 1wherein n≧2, wherein μ_(i) has a known value and wherein the thicknessd_(i) of areas i of said object are determined from equationτ_(i)=μ_(i)σ_(i)d_(i) ².
 5. The method in accordance with claim 1wherein n≧2, wherein σ_(i) has a known value and wherein the thicknessd_(i) of areas i of said object are determined from equationτ_(i)=μ_(i)σ_(i)d_(i) ².
 6. The method in accordance with claim 4wherein said object to be measured has a known homogeneous electricalconductivity σ₀ and a known homogeneous magnetic permeability μ₀ andwherein for every value of i, μ₁=μ₀ and σ₁=σ₀.
 7. The method inaccordance with claim 2 wherein said object to be measured is formed ofa pre-defined material and wherein said method further comprises thestep of generating eddy currents in a test object constructed of saidpre-defined material and having a thickness d_(i)=d₀(i=1, 2, . . . , n)and the step of selecting parameters μ₀ and σ₀ such that V(t)corresponds to a course, over time, of an electromagnetic signalgenerated by said eddy currents in said test object as detected by saidreceiving antenna.
 8. The method in accordance with claim 6 wherein saidobject to be measured is formed of a pre-defined material and whereinsaid method further comprises the step of generating eddy currents in atest object constructed of said pre-defined material and having athickness d_(i)=d₀(i=1, 2, . . . , n) and the step of selectingparameters μ₀ and σ₀ such that V(t) corresponds to said course, overtime, of an electromagnetic signal generated by said eddy currents insaid test object as detected by said receiving antenna.
 9. The method inaccordance with claim 1 wherein i=n=1 and said thickness d of saidobject to be measured is known over an area to be measured, whereinvalues μ_(i) and σ_(i) are determined from equation σ_(i)=μ_(i)σ_(i)d₀².
 10. The method in accordance with claim 1 wherein n>1 and whereinsaid thickness of d₀ of said object to be measured is known and isconstant over an area to measured and for each value of i, d_(i)=d₀ andwherein μ_(i) is determined from τ_(i)=μ_(i)σ_(i)d₀ ².
 11. The method inaccordance with claim 1 wherein n>1 and wherein said thickness of d₀ ofsaid object to be measured is known and is constant over an area to bemeasured and for each value of i, d_(i)=d₀ and wherein σ_(i) isdetermined from τ_(i)=μ_(i)σ_(i)d₀ ².
 12. The method in accordance withclaim 1 wherein α, β, γ, δ, and m are determined from a predeterminedsimulation model wherein said object, said transmit antenna, and saidreceive antenna each have a predefined geometry and are disposed inpredetermined relative positions.
 13. The method in accordance withclaim 1 wherein parameters α, β, γ, δ, and m in a test object havingknown parameters μ_(i), σ_(i), d_(i) and further comprising the stepsof: transmitting a time varying electromagnetic field to said objectfrom a transient antenna for generating eddy currents in said object;detecting signals generated by said eddy currents in a receivingantenna; selecting parameters α, β, γ, δ according to a pre-determinedalgorithm such that V(t) for known values of parameters τ_(i) and$\frac{\sigma_{i}}{\mu_{i}}$

 correspond to a course overtime of electromagnetic signals receivedfrom said test object.
 14. Apparatus for determining properties of anobject to be measured, said apparatus comprising: a transmitter unit; atransmit antenna coupled to said transmitter unit; a receiver unit; areceiver antenna coupled to said receiver unit; and a computer coupledto said transmitter unit and said receiver unit; said computer operativeto control said transmitter to transmit a time varying electromagneticfield to said object for generating eddy current in said object; saidreceiver unit operative to detect an electromagnetic signal S(t) fordetermining parameters τ_(i) and $\frac{\sigma_{i}}{\mu_{i}}$

 such that: $\begin{matrix}{{{S(t)} = {\sum\limits_{i = 1}^{n}{\theta_{i}F_{i}{G_{i}(t)}}}}{with}} & (1) \\{F_{i} = {\delta \sqrt{\frac{\sigma_{i}}{\mu_{i}}}}} & (2) \\{{G_{i}(t)} = \frac{t^{\gamma}}{1 + {{\alpha \left( {\beta \frac{t}{\tau_{i}}} \right)}^{m}^{\beta \frac{t}{\tau_{i}}}}}} & (3)\end{matrix}$

i=1, 2, . . . n   (4)  and $\begin{matrix}{{\sum\limits_{i = 1}^{n}\theta_{i}} = 1} & (5)\end{matrix}$

wherein α, β, γ, δ are real number representing characteristics ofgeometry of said object, said transmitting antenna and said receivingantenna and of relative positions of said object, said transmittingantenna and said receiving antenna and wherein μ_(i) represents magneticpermeability of an area i of said object and σ_(i) represents electricalconductivity of said area i of said object; and wherein said areasi(i=1,2), . . . n) together generate said electromagnetic signal S(t).